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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_11 / Calculate the maximum area of an isosceles trapezoid that has legs of length 1 and one base twice as long as the other. The final answer can be written in the form (m)/(n), where m…

Problem

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problem

Calculate the maximum area of an isosceles trapezoid that has legs of length

1

and one base twice as long as the other. The final answer can be written in the form

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. What is

m^2+n^2

Plain-text mathematical notation (without MathML)

Calculate the maximum area of an isosceles trapezoid that has legs of length 1 and one base twice as long as the other. The final answer can be written in the form (m)/(n), where m and n are relatively prime positive integers. What is m²+n²?

Original LaTeX notation

Calculate the maximum area of an isosceles trapezoid that has legs of length $1$ and one base twice as long as the other. The final answer can be written in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m^2+n^2$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_11
task_id: 7ef548b2-a990-5dd8-a89f-89d8df701a9a
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12B~5fProblems~2fProblem~5f11
task_revision_id: 2
config / split: default / train

Official source

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